Effect of the Interface on the Properties of Composite Media

We develop rigorous bounds on the effective thermal conductivity ${\sigma }_e$ of dispersions that are given in terms of the phase contrast between the inclusions and matrix, the interface strength, volume fraction, and higher-order morphological information, including interfacial statistics. The new bounds give remarkably accurate predictions of the thermal conductivity of dispersions of metallic particles in epoxy matrices for various values of the Kapitza resistance. Corresponding results are obtained for the novel situation in which the inclusions possess a superconducting interface.